Mean-Variance Portfolio Selection With Jump-Diffusion Under Regime-Switching Model

Portfolio theory is one of the classical core theories of mathematical finance.Its key idea is to use portfolio to achieve the purpose of dispersing risk,that is,to maximize profits and minimize risks.Markowitz(1952)pioneered the development of quantitative portfolio selection models and pioneered modern portfolio theory.With the establishment of Markowitz's mean-variance model,many financial and economists at home and abroad began to continuously research the issue of portfolio and achieved great results.In this paper,we first introduce the problem of mean-variance portfolio selection under a hidden Markov regime-switching model.In this model,the appreciation rate of a risky share is modulated by a continuous-time,finite-state hidden Markov chain whose states represent different states of an economy.Then the model is further extended to discuss the portfolio selection with jump-diffusion under regime-switching model,which is more consistent with the actual market economy.In general,we cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes.Based on the separation principle,this paper solves the mean-variance portfolio selection problem and the filtering-estimation problem separately.We also provide robust estimates of the state of chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model.This simplifies the problem of filtering estimation.Finally,an explicit solution to the mean-variance problem is determined using the stochastic maximum principle.